Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method

Haci Mehmet Baskonus; Hasan Bulut; Dilara Gizem Emir

doi:doi:10.11648/j.ml.20150101.11

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Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method

Haci Mehmet Baskonus, Hasan Bulut, Dilara Gizem Emir

Published in Mathematics Letters (Volume 1, Issue 1)

Received: 6 June 2015 Accepted: 18 June 2015 Published: 19 June 2015

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Abstract

In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.

Published in	Mathematics Letters (Volume 1, Issue 1)
DOI	10.11648/j.ml.20150101.11
Page(s)	1-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

The Bernoulli Sub-Equation Function Method, Nonlinear Partial Vakhnenko-Parkes Differential Equation, The Reduced Ostrovsky Equation, Rational Function Solution, Exponential Function Solution, Hyperbolic Function Solution, Complex Trigonometric Function Solution

References

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APA Style

Haci Mehmet Baskonus, Hasan Bulut, Dilara Gizem Emir. (2015). Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Mathematics Letters, 1(1), 1-9. https://doi.org/10.11648/j.ml.20150101.11

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ACS Style

Haci Mehmet Baskonus; Hasan Bulut; Dilara Gizem Emir. Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Math. Lett. 2015, 1(1), 1-9. doi: 10.11648/j.ml.20150101.11

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AMA Style

Haci Mehmet Baskonus, Hasan Bulut, Dilara Gizem Emir. Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Math Lett. 2015;1(1):1-9. doi: 10.11648/j.ml.20150101.11

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@article{10.11648/j.ml.20150101.11,
  author = {Haci Mehmet Baskonus and Hasan Bulut and Dilara Gizem Emir},
  title = {Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method},
  journal = {Mathematics Letters},
  volume = {1},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ml.20150101.11},
  url = {https://doi.org/10.11648/j.ml.20150101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20150101.11},
  abstract = {In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.},
 year = {2015}
}

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TY  - JOUR
T1  - Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method
AU  - Haci Mehmet Baskonus
AU  - Hasan Bulut
AU  - Dilara Gizem Emir
Y1  - 2015/06/19
PY  - 2015
N1  - https://doi.org/10.11648/j.ml.20150101.11
DO  - 10.11648/j.ml.20150101.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20150101.11
AB  - In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.
VL  - 1
IS  - 1
ER  -

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Author Information

Haci Mehmet Baskonus

Department of Computer Engineering, Tunceli University, Tunceli, Turkey
Hasan Bulut

Department of Mathematics, University of Firat, Elazig, Turkey
Dilara Gizem Emir

Department of Mathematics, University of Firat, Elazig, Turkey

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APA Style

Haci Mehmet Baskonus, Hasan Bulut, Dilara Gizem Emir. (2015). Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Mathematics Letters, 1(1), 1-9. https://doi.org/10.11648/j.ml.20150101.11

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ACS Style

Haci Mehmet Baskonus; Hasan Bulut; Dilara Gizem Emir. Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Math. Lett. 2015, 1(1), 1-9. doi: 10.11648/j.ml.20150101.11

Copy | Download

AMA Style

Haci Mehmet Baskonus, Hasan Bulut, Dilara Gizem Emir. Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method. Math Lett. 2015;1(1):1-9. doi: 10.11648/j.ml.20150101.11

Copy | Download

@article{10.11648/j.ml.20150101.11,
  author = {Haci Mehmet Baskonus and Hasan Bulut and Dilara Gizem Emir},
  title = {Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method},
  journal = {Mathematics Letters},
  volume = {1},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.ml.20150101.11},
  url = {https://doi.org/10.11648/j.ml.20150101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20150101.11},
  abstract = {In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Regarding New Complex Analytical Solutions for the Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function Method
AU  - Haci Mehmet Baskonus
AU  - Hasan Bulut
AU  - Dilara Gizem Emir
Y1  - 2015/06/19
PY  - 2015
N1  - https://doi.org/10.11648/j.ml.20150101.11
DO  - 10.11648/j.ml.20150101.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20150101.11
AB  - In this research, a structure of the Bernoulli sub-equation function method is proposed. The nonlinear partial Vakhnenko-Parkes differential equation which is another name the reduced Ostrovsky equation has been taken into consideration. Then, analytical solutions such as rational function solution, exponential function solution, hyperbolic function solution, complex trigonometric function solution and periodic wave solution have been obtained by the same method. All necessary calculations while obtaining the analytical solutions have been accomplished through using commercial wolfram software Mathematica 9.
VL  - 1
IS  - 1
ER  -

Copy | Download